对电声子耦合效应的研究是强关联体系中的重要问题，现有的研究大多集中在自旋无关的情形中。针对自旋相关电声子耦合模型的平均场分析发现，系统的基态是宇称破缺的自旋电流相。尽管这种新颖的宇称破缺相最近引起了广泛的关注和讨论，但是仍然缺少深入地理解和研究。本项目拟采用行列式量子蒙特卡罗方法，对自旋相关电声子耦合模型的基态性质进行细致的研究，并进一步考虑Hubbard型电子间排斥相互作用对整个系统基态的影响。通过非微扰的数值计算，深入探讨其中存在的新颖量子相，并分析相应的量子相变属性。项目研究结果将为目前二维材料中寻找新颖量子物态的实验提供一定的理论支持，同时还能够为新颖量子相间的相变理论研究提供更加丰富的数值证据。

The study of electron-phonon coupling effects is an important problem in strongly-correlated systems. However, existing researches mainly focus on spin-independent cases. The mean-field analysis of the spin-dependent electron-phonon coupling model tells us that the ground state is a parity-breaking spin current phase. Although this novel parity-breaking phase leads to general attentions and discussions recently, there is still a lack of understanding and study in depth. In this project, determinant quantum Monte Carlo method will be used to study the ground state properties of the spin-dependent electron-phonon coupling model in detail. Furthermore, Hubbard-type electron-electron repulsive interaction is considered to study its influence on ground state properties of the whole system. Through non-perturbative numerical calculations, the existing novel quantum phases are studied in depth, and its related nature of quantum phase transitions is analyzed. The results of this project will offer some theoretical supports to experiments for finding novel quantum phases on 2D materials. Meanwhile, they can offer abundant numerical evidences to the theoretical study of phase transitions between novel quantum phases.